Mutual Information and Bose-Einstein Condensation

In the present work we are studying a bosonic quantum field system at finite temperature, and at zero and non-zero chemical potential. For a simple spatial partition we calculate the corresponding geometric entropy and we find that it contains terms originated from genuine quantum as well from classical thermal correlations. After the subtraction of the thermal entropy part, we derive the mutual information for the specific partition. In the case of non-zero chemical potential, we examine the influence of the underlying Bose-Einstein condensation on the behavior of the mutual information, and we find that its thermal derivative possesses a finite discontinuity at exactly the critical temperature.